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Students of music theory may be familiar with the principles of "voice-leading", rules which govern the way in which notes move from one chord to the next. (The rules say the steps should be fairly small.) To help music students understand these concepts, Princeton professor Dmitiri Tymoczko recently developed ChordGeometries, software that generates a 3D musical map in real-time and illustrates how far a piece of music diverges from these rules.
Tymoczko's accompanying paper, "The Geometry of Musical Chords," was published earlier this year in Science and explores voice-leading from the perspectives of both musicology and mathematics. To see the program in action, download one of three demonstration movies or the software itself, available for Mac OSX and Windows XP.